Is there a way to (Cycles) render fire with no emission?
There are a couple of different ways to handle this, depending on the exact result you want. Obviously, if you want no emission at all you can just not include the emission shader in your node graph and just add the "fire" grid (attribute node) onto the "density" grid. It sounds like you want the fire to emit light visibly, just not illuminate anything else?

The easiest way to do that is just use the light path > is camera ray output. Multiply it by your flame grid and it will only appear when viewed by the camera. Here's an example in an otherwise typical fire shader: 

"Is Camera Ray" returns 1 if the ray has originated from the camera, zero any other time. By multiplying it with the flame grid, we essentially delete all data from the flame grid for any ray type other than camera.

If you want the fire to illuminate the smoke plume and show up in reflections, but not light surrounding objects (because let's face it, that's slow and noisy) you can turn off diffuse visibility on the domain object: 

Since we are using ray visbility here, this will also allow us to skip the volume shader calculation entirely for diffuse rays, which might give some extra speedup.